Question

The perimeter and the area of semi-circular plate of radius \[25cm\] are, respectively (Take \[\pi = 3.14\])
A. \[625.5cm,981.25c{m^2}\]
B. \[128.5cm,981.25c{m^2}\]
C. \[412.5cm,981.25c{m^2}\]
D. \[188.5cm,981.25c{m^2}\]

Answer 1

Hint: As we know that the perimeter of circle is given as \[2\pi r\]and area of circle is \[\pi {r^2}\]. Hence, we apply the same concept for semi-circle, it’s perimeter can be given \[\pi r + 2r\]means that‘s the perimeter of half-circle plus its diameter, and the area of semicircle can be given as \[\dfrac{{\pi {r^2}}}{2}\]. So, on substituting the value of radius in the above formula hence required answer will be obtained.

Complete step by step answer:

As the given radius is \[25cm\]and we have to take the value as \[\pi = 3.14\].
Diagram:

The perimeter of semi-circle can be given as \[\pi r + 2r\]
So, putting both the values in the above formula as
\[p = \left( {3.14} \right)\left( {25} \right) + 2\left( {25} \right)\]
On simplifying, we get,
\[p = 50 + 78.5\]
On addition,
\[p = 128.5cm\]
And now calculating the area of semi-circle so it will be given as \[A = \dfrac{{\pi {r^2}}}{2}\]
On substituting the above values,
\[A = \dfrac{{\left( {3.14} \right){{\left( {25} \right)}^2}}}{2}\]
On simplifying, we get,
\[A = \dfrac{{\left( {3.14} \right)625}}{2}\]
On calculating the value will be,
\[A = 981.25c{m^2}\]
Hence, option (B) is our required correct answer.

Note: For the perimeter of semicircle don’t forget to add the value of the diameter, otherwise, you will obtain the incorrect solution for the given problem.
answer. In mathematics, a semicircle is a one-dimensional locus of points that forms half of a circle. The full arc of a semicircle always measures 180°. It has only one line of symmetry.